Due to the COVID-19 crisis, the information below is subject to change,
in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).

5 credits

22.5 h + 7.5 h

Q2

Teacher(s)

Lauzin Clément;

Language

English

Main themes

The teaching unit covers three themes. The first part gives an overview of the molecular Hamiltonian and the separation of variables. The second part is dedicated to group theory and the use of the symmetry in order to simplify molecular physics problems and the third focuses on different applications.

Aims

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a. Contribution of the teaching unit to the learning outcomes of the programme (PHYS2M and PHYS2M1)AA 1.1, AA1.2, AA1.3, AA 1.5, AA 1.6, AA 2.1, AA2.3, AA 3.1, AA 5.2 b. Specific learning outcomes of the teaching unit At the end of this teaching unit the student will be able to : 1. determine the symmetry of a molecule and use it in order to construct symmetry adapted wavefunctions ; 2. use the symmetry and the Pauli principle to rationalize the intensity of a molecular absorption spectrum ; 3. solve a Hückel problem ; 4. understand the basic concepts of molecular dynamics calculations. |

Content

The teaching unit is structured as follows :

It is worth stressing that, all along the lectures, the symmetry of the molecules will be used to solve molecular physics problems, thus providing at the same time an interesting and concrete scope of application of group-theoretical tools.

- Structural and dynamical properties of molecules : polyatomic molecular Hamiltonians, separation of the electronic and nuclear motions, molecular coordinates, adiabatic and diabatic representations, conical intersections.
- Group-theoretical determination of molecular structure : introduction and general theory, classification of the electronic, vibrational, rotational and nuclear spin states of molecules.
- Introduction to quantum chemistry : molecular Hartree-Fock equations, LCAO (Linear Combination of Atomic Orbitals) method, Roothaan-Nesbet-Pople equations, electronic configurations.
- Various applications to illustrate the lectures : molecular spectroscopy, time-dependent methods applied to molecular quantum dynamics, “hands-on” introduction to molecular dynamics codes (e.g. MCTDH).

It is worth stressing that, all along the lectures, the symmetry of the molecules will be used to solve molecular physics problems, thus providing at the same time an interesting and concrete scope of application of group-theoretical tools.

Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Lectures and 2 laboratories (1 experimental and 1 theoretical)
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Written or oral exam or written report.
Bibliography

P. Bunker, P. Jensen, Molecular Symmetry and Spectroscopy ,

D.J. Tannor, Introduction to Quantum Mechanics- A Time-Dependent Perspective (2007) University Science Books .

F.Gatti, B.Lasorne, H.-D.Meyer, A.Nauts, Applications of Quantum Dynamics in Chemistry, (2017) Springer.

**(2006) NRC Research Press. ISBN 978-0-660-19628-2.**D.J. Tannor, Introduction to Quantum Mechanics- A Time-Dependent Perspective (2007) University Science Books .

F.Gatti, B.Lasorne, H.-D.Meyer, A.Nauts, Applications of Quantum Dynamics in Chemistry, (2017) Springer.

Faculty or entity

**PHYS**